The Alexandria City Council voted last night to allow a horse-drawn sightseeing car and horse-drawn carriages to be hired out to hoof through Old Town, at least for the summer.

The council voted 6 to 1 to approve temporary permits for one horsecar sightseeing vehicle and four horse-drawn carriages, provided all the horses wear diapers.

"We want to keep the horse manure in the City Code, where it belongs," said council member Donald C. Casey, causing a ripple of laughter through the council chamber. Casey and Mayor Charles E. Beatley, both Democrats who were defeated in the May 7 election, attended their final meeting last night before the newly elected council takes office next Monday.

Only council member Margaret B. Inman (R) objected to the horses' trial run, citing the potential traffic snarls that four-legged animals might cause.

The permit approved last night expires Sept. 30. In the meantime, the council has asked City Attorney Des Calley to draft an ordinance governing horse-drawn vehicles.

In September, John Lender, owner of Capital Horsecars, and Donald W. Leach, owner of Classic Carriages, must reapply for their right to operate the horse-drawn vehicles in Alexandria. Lender said his sightseeing vehicles would carry 20 to 24 people through Old Town. Leach's carriages will hold four people.

The permit the council approved forbids loud music and eating during the tours and prohibits the horses from operating during rush hour or ambling along U.S. Rte. 1 and South Washington Street, two heavily traveled thoroughfares.

In other action, the council unanimously authorized Acting City Manager Vola T. Lawson to negotiate a contract for public official liability and law enforcement insurance at a cost about 500 percent higher than the city's current insurance.

The city's insurance policies, which cost $54,845, expire July 1. Lawson said that because the price of insuring a city, its elected officials and police officers is skyrocketing nationwide owing to million-dollar lawsuit settlements, Alexandria is exploring ways to insure itself. But at least for next year, Lawson said she would negotiate a contract with Republic Insurance that will give Alexandria half of its 1984 coverage, $1 million, for a premium of $234,234.

The council also voted to allow myotherapists, therapists who apply pressure to muscles for pain relief, to practice in the city. Alexandria's massage parlor ordinance previously prohibited myotherapy.

The council also reappointed three current school board members, Lynnwood C. Campbell, Sandra K. Lindsay and Timothy S. Elliott. Lindsay and Elliott were reappointed unanimously and council member Carlyle C. Ring cast the only vote againt Campbell. The school board has nine members, three of whom are up for reappointment annually.